Answer
please see image
Work Step by Step
$f(x)=|x|$
(Using desmos.com) we graph f(x) (blue dashed graph).
By hand, plot the points
(-2,2), (-1,1), (0,0), (1,1), (2,2)
and the two rays which make the graph of f.
$g(x)=-f(x+4)+1,$
so the graph of $g$ (solid red line) is obtained from the graph of f by
shifting it left by $4$ units,
then, reflecting across the x-axis ($g_{1}(x)$ on the image).
and, finally, raising up by 1 unit (red solid line).
Using the above points, $(x,f(x))$
plot $(x-4$, $-f(x)+1)$ and join.